Planar transmission-line permittivity sensor and calibration method for the characterization of liquids, powders and semisolid materials

ABSTRACT

A low cost planar transmission line sensor and simple calibration method for measuring the complex permittivity of materials with minimal sample preparation over a wide band of radio- and microwave frequencies. The sensor is also used for measuring anisotropic dielectric properties of materials with a defined grain.

REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/043,659, filed Aug. 29, 2014 entitled“Permittivity Planar Transmission-Line Sensor and Calibration Method forthe Characterization of Liquids, Powders, and Semisolid Materials”. TheU.S. Provisional Patent Application Ser. No. 62/043,659 is hereinincorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a sensor apparatus and a calibrationmethod for measuring the complex permittivity of liquids, powders, andsemisolid materials with planar transmission lines at radio- andmicrowave-frequencies. Furthermore the present invention relates to amethod for measuring the anisotropic dielectric properties of materialswith the sensor apparatus.

BACKGROUND OF THE INVENTION

The permittivity of a material describes the relationship betweenelectric flux density and an applied electric field. Permittivity is afunction of frequency and the physical and molecular properties of anymaterial. If a relationship between the material permittivity and aphysical property of interest can be established, permittivitymeasurements can be used to infer the measurement of several attributesof, for example, agricultural and food materials, solvents,pharmaceutical materials. This has been used successfully in themeasurement of several attributes of agricultural products such as, forexample, the water content of grain (Trabelsi and Nelson, IEEE Trans. OnInstrumentation and Measurement, Volume 55 (3), 953-963, 2006; Nelsonand Trabelsi, Trans. ASABE, Volume 55 (2), 629-636, May 2012; Kraszewskiet al., Meas. Sci. Technol., Volume 8, 857-863, 1990), and the fatcontent of fish (Kent, Food Control, Volume 1, 47-53, 1990). Morerecently (Duhamel et al., Proc. IEEE MTT-S Int. Microwave Sym. Dig.,Denver, Colo., USDA, 107-110, 1997; Joines et al., Me. Phys., Volume 21,547-550, April 1994; Trabelsi and Nelson, American Society ofAgricultural and Biological Engineers, St. Joseph, Mich., ASABE PaperNo. 097305, 2009; Trabelsi and Roelvink, Journal of Microwave Power andElectromagnetic Energy, Volume 48 (4), 215-220, 2014), there has been afocus on using the permittivity of biological materials to identifyphysical properties such as healthy or diseased human breast tissue(Joines et al., April 1994, supra), or the quality attributes of poultrymeat (Trabelsi and Nelson, 2009, supra).

The complex relative permittivity of a material, ε*, is an intrinsicelectrical property that relates the electric flux density within thematerial to an applied electric field. The relative complex permittivityis often written as ε*=ε′jε″, where ε′ is the dielectric constant and ε″is the dielectric loss factor. The permittivity (or dielectricproperties) is a function of the physical properties of a material, suchas the moisture and density of granular and particulate materials. If arelationship between the permittivity and a physical property ofinterest can be established, permittivity measurements can be used as anindirect, non-destructive method of inferring physical properties. Inindustrial RF and microwave heating applications, the knowledge of thepermittivity of the material to be heated allows rigorous analytical andnumerical design of heating cavities and other electromagnetic heatingapparatus. The development of sensors and techniques for accurately andefficiently measuring the permittivity of agricultural and biologicalmaterials is therefore an area of research with significant commercialpotential.

Relationships between the physical and dielectric properties ofmaterials have been reported in several previous studies. Examples foragricultural products are sensors for measuring the water content ofgrain (Nelson and Trabelsi, ASABE, Volume 55(2), 629-636, 2012), or thefat content of fish (Kent, Food Control, Volume 1, 47-53, 1990).Examples for biological materials are methods for inferring qualityattributes of poultry meat (Trabelsi and Nelson, ASABE Paper No. 097305,American Society of Agricultural and Biological Engineers, 2009) ordifferences between normal and diseased human breast tissue (Joines etal., 1994, supra). The permittivity of biological tissue such as poultrymeat depends on a number of factors related to the quality parameters,such as water holding capacity and pH (Trabelsi and Nelson, 2009, supra;Trabelsi, American Society of Agricultural and Biological Engineers,2012, ASABE Paper No. 121337363). Such properties can vary over a givensample volume, thus the permittivity of poultry meat is oftenheterogeneous and anisotropic (Clerjon and Damez, Meas. Sci. Technol.,Volume 18, 1038-1045, 2007). The degree of anisotropy is a parameterthat can be used to estimate parameters such as tissue age (Damez et al,Journal of Food Engineering, Volume 85, 116-122, 2008) or the differencebetween fresh and frozen meat (Clerjon and Damez, 2007, supra). Aconvenient measurement method for characterizing dielectric anisotropyof materials would be very useful.

Many techniques have been developed for determining the permittivity ofmaterials (Baker-Jarvis et al., IEEE Trans. Microwave Theory Tech.,Volume 38 (8), 1096-1103, August, 1990; Pournaropoulos and Misra, Meas.Sci. Technol., Volume 8 (11), 1191-1202, 1997; Knöchel et al., Meas.Sci. Technol., Volume 18 (4), 1061-1068, 2007; Baker-Jarvis et al., NISTTech. Note 1536, 2005), some of which have been implemented asindustrial sensors (Nyfors and Vainikainen, Industrial MicrowaveSensors. Norwood, Mass., USA: Artech House, 1989). Perhaps the mostcommonly utilized modern method for measuring the permittivity ofliquids involves the use of an open-ended coaxial-line probe(Pournaropoulos and Misra, 1997, supra). Its popularity is largely dueto relatively simple calibration procedures (Kraszewski et al., IEEETrans. Instrum. Meas., Volume 32 (2), 385-387, June 1983), its abilityto measure over a wide range of frequencies, and its commercialavailability (Agilent-Technologies, Agilent 85070E Dielectric Probe Kit:200 MHz to 50 GHz Technical Overview). However, to measure thepermittivity of water-based materials, which have relatively largedielectric constants, the coaxial-line probe must be relatively small toavoid radiation effects (Wei and Sridhar, Proc. IEEE MTT-S Int.Microwave Symp. Dig., Albuquerque, N. Mex., USA, 1271-1274, 1992; Weiand Sridhar, IEEE Trans. Microwave Theory Tech., Volume 39 (3), 526-531,March 1991). Therefore, for biological materials, only a small volume ofmaterial can be measured (Hagl et al., IEEE Trans. Microwave TheoryTech., Volume 51 (4), 1194-1206, April 2003). In addition, theopen-ended coaxial-line probe cannot be conveniently used tocharacterize the dielectric anisotropy of materials, (Clerjon and Damez,Meas. Sci. Technol., Volume 18, 1038-1045, 2007).

Transmission lines are often used to measure the broad-band complexpermittivity of liquid and semisolid materials (Baker-Jarvis et al.,IEEE Trans. Microwave Theory Tech., Volume 38, 1096-1103, 1990). Themeasurement is typically made by placing the material in a section oftransmission line and measuring the two-port complex scatteringparameters over a range of frequencies. The complex line propagationconstant, γ, can be obtained from the scattering parameters by variousmethods. The complex relative permittivity of the material can then befound from a model that relates ε* to γ. This model is dependent on thetransmission-line dimensions and type, e.g., waveguide, coaxial line,planar line. Compared to the open-ended coaxial-line probe, thesetransmission line arrangements offer the advantage of measuring theaverage permittivity of the material along the length of line. Thesensing length, and therefore the material volume, can be large relativeto volumes sensed by open-ended coaxial-line probes. However, the closedstructures of many of these transmission line types, (e.g., waveguideand coaxial line) mean that considerable sample preparation isnecessary. Closed transmission lines cannot be conveniently used tomeasure the permittivity of materials outside a laboratory.

Planar transmission lines, such as coplanar waveguide(CPW), can beconfigured as permittivity sensors (Stuchly and Bassey, Meas. Sci.Technol., Volume 9, 1324-1329, 1998). The open structure of thesetransmission lines requires relatively less sample preparation comparedto closed transmission-line types because the sample material can beeasily placed in contact with the lines without needing to mechanicallyconnect a section of sample-filled transmission line. To numericallyextract ε* from γ, either closed-form approximations for the CPWparameters (Roelvink and Trabelsi, IEEE Trans. Instr. Meas., Volume 62(11), 2974-2982, 2013; herein incorporated by reference in its entirety)or full-wave numerical techniques can be applied (Huynen et al., IEEETrans. Microwave Theory Tech., Volume 42 (11), 2099-2106, 1994).However, a significant limitation of these approaches is that neitherallows ε* to be directly calculated from γ, and numerical iterativemethods must be used. Moreover, it has been demonstrated for planar lineparameters (Roelvink and Trabelsi, IEEE Trans. Instr. Meas., 2013,supra), that the ε* extracted from such an approach is very sensitive tothe line dimensions, particularly for materials with relatively largedielectric constants, such as water-based biological materials. A smalluncertainty in these dimensions can result in considerable uncertaintyin the measured ε*. If the planar lines are fabricated with low-costequipment, the dimensional uncertainty is often large. For suchsituations an alternative approach such as a calibration procedure forextracting ε* that does not required a precise knowledge of the linedimensions would be very useful.

Existing methods for measuring the permittivity tensor of materials withanisotropic dielectric properties generally operate by placing a samplein a section of waveguide or coaxial transmission line and measuring thetwo-port scattering parameters with the sample ‘grain’ oriented in twoways; parallel and perpendicular to the transverse electric fieldcomponent of the propagating wave (Akhtar et al., IEEE Trans. MicrowaveTheory Tech., Volume 54, 2011-2022, 2006; Torgovnikov, DielectricProperties of Wood and Wood-Based materials, Wood Science, ed. Timell,1993, Berlin: Springer-Verlag). These methods require that the sample becarefully prepared and are mechanically time consuming. Moreover, forbiological materials such as muscle tissue, it can be difficult toprecisely identify the direction of the grain. If the sample is notproperly aligned, this approach does not provide an accurate measurementof the permittivity tensor. The high level of precision means that suchan approach is not well suited to measurements outside the laboratory.

There have been a number of studies that use planar or striptransmission lines to measure permittivity. Stuchly and Bassey (1998,supra) investigated the use of CPW for measuring ε′. In their study, ε′was determined by a technique that did not account for the source andload mismatch terms associated with the line or the sample-edgediscontinuities. While suitable when ε′ is small, for the larger ε′ ofbiological materials a different approach is required.

Raj et al. (IEEE Trans. Instrum. Meas., Volume 50 (4), 905-909, August2001) considered measuring liquids with a multilayered CPWconfiguration. To calibrate their sensor, as well as accounting for thesample-edge discontinuities, a set of calibration liquids with known ε*was measured, and empirical curve fitting was used. The empiricallyobtained curves are a function of the CPW dimensions and, therefore, newcurves are needed for any change in dimension.

Huynen et al., (IEEE Trans. Instrum. Meas., Volume 50 (5), 1343-1348,October 2001) investigated the use of the multiline (Engen and Hoer,IEEE Trans. Microwave Theory Tech., Volume 27 (12), 897-903, December1979; Marks, IEEE Trans. Microwave Theory Tech., Volume 39 (7),1205-1215, July 1991) or line-line (Huynen et al, October 2001, supra)technique to measure the propagation constant of a microstrip lineformed on a low-loss laminate substrate material. The multilinetechnique determines γ by measuring two transmission lines that areidentical, apart from a known length difference. This technique istherefore attractive for use with planar transmission lines, because γcan be determined independent of any discontinuities. A numericalanalysis (Huynen et al., October 2001, supra), based on a variationalformulation (Huynen et al., IEEE Trans. Microwave Theory Tech., Volume42 (11), 2099-2106, November 1994) was used to extract the substratepermittivity from the measured propagation constant. While theconfiguration (Huynen et al, October 2001, supra) is suitable forpermittivity measurements of substrate materials, it is not mechanicallysuited to the measurement of materials placed on the planar line becauseconsiderable sample preparation is necessary to ensure that the twosamples are identical, apart from a known length difference. Inaddition, the method adopted for the numerical extraction of thematerial permittivity requires significant computational resources.

The permittivity of a material is a function of its physical properties.Numerous techniques and configurations have been used to measure thepermittivity of materials, as described above. For planartransmission-line sensors, there are several ways to extract ε* from themeasured γ. One way is to use numerical techniques such as thespectral-domain technique (Huynen et al., 1994, supra) or the“method-of-moments” (Sonnet, www.sonnetsoftware.com). Numericaltechniques, however, require considerable computational resources inorder to obtain accurate results and therefore they are not particularlysuited for rapid permittivity measurements in industrial settings.Another approach is to use analytic models that relate the linedimensions/parameters to γ (Roelvink et al., 2013, supra; Stuchly andBassey, 1998, supra; Raj et al., August 2001, supra). Such models canprovide accurate results if the line dimensions/parameters are known.However, as demonstrated (Roelvink and Trabelsi, 2012 IEEE InternationalSymposium on Antennas and Propagation and USNC-URSI National RadioScience Meeting, Chicago, Ill., 2012; herein incorporated by referencein its entirety), small dimensional uncertainties, particularly inregions where the fields are relatively concentrated, can result inlarge measurement uncertainty. This uncertainty increases as thedielectric constant ε′ of the material increases (Roelvink and Trabelsi,Symposium and Meeting 2012, supra). If low-cost equipment is used tomanufacture the planar transmission-line sensor, the dimensionaluncertainty can be large. For such situations, an alternative approachfor extracting ε* from γ that does not require a precise knowledge ofthe line dimensions would be useful.

While various methods have been developed for measurement of propertiesof different materials, there remains a need in the art for a method forrapid, non-destructive, wideband permittivity measurements of materialssuch as liquids, powders, and semi-solid materials, especially thosewithout uniform edges. There also remains a need in the art for a simplemethod for measuring the permittivity of materials with anisotropicproperties. There also remains a need in the art for a simplecalibration procedure for determining the material permittivity from thepropagation constant measured with planar transmission lines. Thepresent invention provides a simple two standard calibration techniqueand low-cost planar transmission-line sensor apparatus for rapidpermittivity measurements on liquid, powders, and semisolid materials,which requires minimal sample preparation. It is also well suited foruse in industrial environments as a sensor to determine moisture anddensity of powdered materials, quality parameters of food products suchas meat, powdered foods, foods with a semi-solid consistency, and forcharacterization of biological materials to determine the physicalproperties of the material, such as the presence or absence of disease.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a sensorapparatus, based on planar transmission lines, for rapid permittivitymeasurements for materials including materials without uniform edges,such as for example, liquid, powders, and semisolid materials withminimal sample preparation.

Another object of the present invention is to provide a calibrationmethod that allows the direct determination of the material permittivityfrom the measured microwave scattering parameters with planartransmission lines.

A still further object of the present invention is to provide anaccurate and simple method for the use of planar transmission lines tomeasure the anisotropic dielectric properties of materials that can berepresented by a uniaxial permittivity tensor. Once the components ofthe permittivity tensor are determined, they can be used for rapid andnondestructive determination of physical properties of interest offoods, agricultural products and other biological and non-biologicalmaterials. Examples of applications include, but are not limited to,meat freshness, internal defects in agricultural products, presence ofcontaminants, and abnormalities in biological tissues. Examples of suchmaterials are meat, timber and many wood products, some fruits, andother materials with a defined grain. These properties can be used todetermine material parameters such as age or the difference betweenfresh and frozen food products.

Further objects and advantages of the present invention will be apparentfrom the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a sectional view of coplanar waveguide (CPW)transmission line showing relevant line parameters such as t, h, b, anda.

FIGS. 2A-2C are drawings showing three views of planartransmission-line-sensor apparatus 10. FIG. 2A is a top view including along 16 and a short 14 planar transmission line, feed lines 20,substrate ε_(s) 30, vias 22, and planar line lengths l₁ and l₂. FIG. 2Bis a bottom view of apparatus 10 showing feed lines 20. FIG. 2C is a topview of apparatus 10 showing a sample holder 26 and liquid sample 28sitting on substrate and over planar lines 14 and 16.

FIG. 3A is a drawing of a material having a uniaxial permittivitytensor. Materials with a grain such as wood and muscle tissue can berepresented by a uniaxial permittivity tensor. Cartesian coordinatesystem are shown relative to the sensor (x,y,z) and the material(u,y,w). FIG. 3B is a drawing showing coplanar lines 14 and 16 withinner track width a, outer track width b, and conductor thickness t,feed lines 20 and vias 22, substrate 30 with permittivity ε_(s), andheight h. The planar line lengths are l₁ and l₂.

FIG. 4 is a photograph of a CPW sensor 10 showing CPW planar lines 14and 16, substrate 30, and microstrip-to-coaxial line transitions 24.

FIG. 5 is a block diagram of the planar transmission line sensor andassociated measurement hardware.

FIGS. 6A and 6B are graphs showing the calibration constants d* and c*as a function of frequency, calculated with calibration standards ofε₁*=1 (air) and distilled water for ε₂*. The real parts of d*and c* areshown in FIG. 6A and the imaginary parts of d* and c*are shown in FIG.6B.

FIGS. 7A and 7B are graphs comparing results for ε* as a function offrequency for cyclohexane. FIG. 7A shows ε′ dielectric constant on yaxis and FIG. 7B shows ε″ dielectric loss factor on y-axis.

FIGS. 8A and 8B are graphs comparing results for ε* as a function offrequency for ethanol and 75/25% ethanol/water mixture at 20 degrees C.FIG. 8A shows ε′ dielectric constant on y axis and FIG. 8B shows ε″dielectric loss factor on y-axis.

FIGS. 9A and 9B are graphs comparing results for ε* as a function offrequency for 50/50% and 25/75% ethanol/water mixtures at 20 degrees C.FIG. 9A shows ε′ dielectric constant on y axis and FIG. 9B shows ε″dielectric loss factor on y-axis.

FIG. 10 is a graph showing results calculated from simulations comparedto those predicted with ε_(meas)*(θ)=ε_(u)*cos² θ+ε_(w)*sin² θ at 2 GHz.

DETAILED DESCRIPTION OF THE INVENTION

Dielectric methods are commonly used for rapid nondestructivemeasurement of attributes of products such as moisture content, fatcontent in agricultural products and food, lumber, chemical,pharmaceutical, concrete, and construction industries. The essence ofdielectric methods is based on the electric field-material interactionwhich is characterized by the dielectric properties (complexpermittivity). These properties can be highly correlated to the desiredattributes of a material. The dielectric methods are useful because theelectric field used by the sensing instruments penetrates materialswell, providing volumetric sensing.

The present invention is a planar waveguide transmission-line sensor formeasuring the wideband complex permittivity of liquids, powders, andsemisolid materials such as biological materials at radiowavefrequencies, microwave frequencies and millimeter-wave frequencies.Another aspect of the present invention is a new calibration method forplanar waveguide transmission lines to provide a method for determiningthe material permittivity from the measured scattering parameters. Athird aspect of the present invention is a method for measuring thedielectric anisotropy of materials with a defined grain, such as meat,wood, fruits, for example. The amount of anisotropy can be used todetermine material parameters such as for example, tissue age, diseasestates of tissues, differences between fresh and frozen food products.

For planar transmission lines, the measured line propagation constantcan be expressed as

γ=α+jβ=α _(d)+α_(r)+α_(c) +jβ  (1)

where j=√{square root over (−1)}, β is the phase constant (rad/m) and αis the attenuation constant (np/m), which consists of α_(d), α_(r),α_(c); namely, the dielectric, radiation, and conductor attenuationconstants, respectively (surface-wave losses are assumed to benegligible). All components in (1) are functions of the planar linedimensions, operating frequency, and material permittivity, ε*. Theproblem can be separated into two parts: determination of γ fromscattering parameter measurements and determination of ε* from γ. Thefirst object of this invention is to provide a calibration procedure forthe direct determination of ε* from γ. This procedure is outlined in thefollowing section. For clarity, it is first necessary to describe how γcan be measured with planar transmission lines with the multiline orline-line technique (Janezic and Jargon, IEEE Microwave and Guided WaveLetters, Volume 9, 76-78, 1999). The second object of this invention isto provide a planar transmission-line sensor configuration forconveniently measuring the line propagation constant γ with themultiline technique. This object is described in Section 2. The thirdobject of the present invention is to provide a method for measuring thedielectric anisotropy of materials. This method is disclosed in Section3.Dielectric Calibration Method with Planar Transmission Lines

Determining γ

To determine the line propagation constant, γ, with the multilinetechnique (Janezic and Jargon, 1999, supra), two or more transmissionlines are used that are identical, apart from a known length difference.The propagation constant γ is calculated from uncalibrated scatteringparameter measurements of each transmission line. The multilineexpressions are for two transmission lines with a length differencel_(diff)=l₂−l₁ are (Janezic and Jargon, 1999, supra):

$\begin{matrix}{\gamma = {\frac{\ln \left( \lambda_{av} \right)}{l_{diff}} + {j\frac{2\; \pi \; n}{l_{diff}}}}} & (2) \\{\lambda_{av} = {\frac{1}{2}\left( {\lambda_{1} + \frac{1}{\lambda_{2}}} \right)}} & (3) \\{\begin{pmatrix}\lambda_{1} \\\lambda_{2}\end{pmatrix} = \frac{M_{11} + {M_{22} \pm \sqrt{\left( {M_{11} - M_{22}} \right)^{2} + {4M_{12}M_{21}}}}}{2}} & (4) \\{M = {T_{l\; 1}\left\lbrack T_{l\; 2} \right\rbrack}^{- 1}} & (5)\end{matrix}$

λ₁ and λ₂ are the eigenvalues of matrix M, while T_(l1) and T_(l2) arethe transmitting matrices for the transmission lines of length l₁ andl₂, respectively, which are obtained from the two-port scatteringparameters (Janezic and Jargon, 1999, supra), measured with aappropriate hardware, such as for example a vector analyzer. If l_(diff)is less than one-half wavelength, n=0 in (2). If l_(diff) is more thanone-half wavelength, n is an integer whose value can be obtained bycomparing several possible solutions for β at two frequencies (Roelvinket al., 2013, supra). An advantage of the multiline technique is thatdiscontinuities on the transmission lines, such as those caused by thesample edges or sample holder, do not need to be modeled.

1.2 Determining ε* from γ

From transmission-line theory (Rizzi, Microwave engineering: PassiveCircuits, 1988, New Jersey, USA: Prentice-Hall), the propagationconstant due to the ‘effective’ complex relative permittivity of thematerial/line combination, ε_(eff)*, is,

γ_(d)=α_(d) +jβ=jβ ₀√{square root over (ε_(eff)*)}  (6)

where β₀=2πf/c is the free-space phase constant (rad/m), f is thefrequency (Hz) and c=2.99792×10⁸ m/s is the speed of light in freespace. ε_(eff)* is a function of the material and substratepermittivity, as well as the planar line dimensions and type. By way ofan example, a cross section view of the CPW transmission line is givenin FIG. 1, showing a coplanar waveguide transmission line with innertrack width a, outer track width b, and conductor thickness t, feedlines and vias, substrate with permittivity ε_(s) and height h. If thesubstrate permittivity and line dimensions are known, quasi-staticanalyses (Gupta et al., Microstrip Lines and Slotlines, 1979, Dedham:Artech House) or numerical techniques (Huynen et al., IEEE Trans.Microwave Theory Tech., Volume 42 (11), 2099-2106, 1994; Itoh and Mitra,IEEE Trans. Microwave Theory Tech., Volume 21, 496-499, 1973) can beused to obtain ε_(eff)* in terms of ε*. However, the dimensionaluncertainty can result in large measurement uncertainty (Roelvink andTrabelsi, 2013, supra). The present invention provides a calibrationtechnique that does not require the substrate permittivity or the planarline dimensions to be known.

With the material placed in direct contact with the planar lines, theconformal mapping technique (Gupta et al., 1979, supra), or numericaltechniques (Itoh and Mittra, 1973, supra), can be used to show thatε_(eff)* is a linear function of ε*, namely,

ε_(eff) *=mε*+c*  (7)

where the slope m is a scalar quantity that is a function of the planarline dimensions and is independent of frequency if the planar linedispersion is negligible. m approaches a value of 0.5 as the conductorthickness tends to zero (Roelvink and Trabelsi, 2013, supra; Gupta etal., 1979, supra). c* is a function of the planar line dimensions andthe substrate permittivity, ε_(s)*, which typically has some dielectricloss, and hence c* is a complex quantity. Equation (7) is appropriatefor CPW, conductor-backed CPW, and two- or three-coplanar strips Guptaet al., 1979, supra).

If the combined radiation and conductor losses, α_(r)+α_(c), are assumedto be negligibly small, two measurements of γ for materials with knownε* are sufficient to determine m and c*. This was the approach reportedin Roelvink and Trabelsi, IEEE International Instrumentation andMeasurement Technology Conference (12MTC 2013); herein incorporated byreference in its entirety, where it was found that neglecting theselosses resulted in significant error. In the present invention, ratherthan assuming α_(r)+α_(c)=0, the losses are assumed to be of the form(Haydl et al., Attenuation of millimeterwave coplanar lines on galliumarsenide and indium phosphide over the range 1-60 GHz, In: IEEE Int.Microwave Symp., Dig., 1992)

α_(r)+α_(c) ≈aRe(√{square root over (ε*)})  (8)

where Re(*) denotes the real part of * and a is a scalar, which is afunction of the operating frequency, the substrate permittivity, and theplanar line dimensions. Equation (8) was obtained from experimentalmeasurements of CPW on low-loss dielectric substrates over a large rangeof microwave frequencies (Haydl et al., 1992, supra; Ponchak et al.,IEEE Trans. Microwave Theory Tech., Volume 47, 241-243, 1999) and ismore appropriate than the form obtained with the closed-form expressionsused in (Roelvink, et al, 2013, supra). To determine the constants in(7) and (8), three measurements of γ with known ε* can be made. However,some simplification is possible: By recognizing that, for high-lossmaterials α_(d)>>α_(r)+α_(c), while for low-loss materials a Re(√{squareroot over (ε*)})≈a√{square root over (ε*)}, (6)-(8) can be substitutedinto (1) and, after some simplification,

$\begin{matrix}{ɛ^{*} = {- {\frac{1}{d^{*}}\left\lbrack {\left( \frac{\gamma}{\beta_{0}} \right)^{2} + c^{*}} \right\rbrack}}} & (9)\end{matrix}$

where d*≈m−j2a√{square root over (m)}/β₀. The imaginary part of d*accounts approximately for the effect of the conductor and radiationlosses, which are often significant, particularly for calculating ε″.Equation (9) is an equation of a straight line with slope −1/d* andintercept −c*/d*. The two complex quantities can be obtained from twomeasurements of γ for materials with known ε*, namely,

$\begin{matrix}{d^{*} = \frac{\gamma_{1}^{2} - \gamma_{2}^{2}}{\beta_{0}^{2}\left( {ɛ_{1}^{*} - ɛ_{2}^{*}} \right)}} & (10) \\{c^{*} = {\left( \frac{\gamma_{1}}{\beta_{0}} \right)^{2\;} - {d^{*}ɛ_{1}^{*}}}} & (11)\end{matrix}$

where the subscripts refer to each measured material. Natural choicesfor the calibration standards are air, ε′=1, and a reference liquid,such as distilled water (Kaatze, Meas. Sci. Technol., Volume 18,967-976, 2007) and it is found that these standards give relativelysmall measurement uncertainty (Roelvink et al, Meas., Sci. Technol.,Volume 24, 1-8, 2013; herein incorporated by reference in its entirety).This simple calibration procedure yields very accurate results for alarge range of microwave frequencies and materials. An example of howthis technique can be applied is given in Example 1.

2. Planar Transmission-Line Sensor Apparatus

The planar transmission-line sensor apparatus 10 shown in FIGS. 1-4includes a metal-clad substrate 30, short planar transmission line 14,long planar transmission line 16, board top side 18, board bottom side19, feed lines 20, plated through-hole via 22, microstrip-to-coaxialline transition 24, and sample holder 26 if needed for liquid samples.

The multiline technique for determining γ can be used with transmissionlines 14 and 16 that contain discontinuities, such as those introducedby the plated through-hole vias 22 connecting the board bottom side andthe board top side, the only requirement being that the two lines 14 and16 are identical except for the known length difference l_(diff). Thisremoves the need to explicitly model the effect of the discontinuities.FIG. 2 depicts an example of a transmission-line arrangement. FIG. 2shows an arrangement made on a double-sided printed circuit board, withplanar transmission lines 14 and 16 etched or milled on the board topside 18 (FIG. 2(A)) and connected to two feed lines 20 which are etchedor milled on the board bottom side 19 (FIG. 2(B)) by a means forconnecting transmission lines such as, for example, plated through-holevia 22, metal post (not shown) or other connections such as tabinter-connects, or inductively-coupled transitions. The advantage ofthis arrangement is that as long as the sample material has a flat facethat completely covers the two planar lines, the sample edges areremoved from the planar line fields. Hence, this arrangement can be usedto measure materials with irregular edges, such as semisolid biologicalmaterials. If a sample holder 26 is required in the case of liquidsamples 28, it can be positioned away from the planar lines 14 and 16where it will not affect the measurement as shown in FIG. 2(C). Tominimize the impedance mismatch, the feed-line 20 and planar-line 14 and16 dimensions are chosen to have a characteristic impedance ofapproximately 50Ω. For the planar line, these dimensions are selectedwith the expected dielectric constant of the sample material in place.

The error in γ calculated with equation 2, due to linear errors in theeigenvalues, decreases as the line length difference, l_(diff),increases (Marks, IEEE Trans. Microwave Theory Tech., Volume 39 (7),1205-1215, 1991). However, if one of the lines is made too long, thetransmitted signal will be comparable to the noise floor of themeasurement instrument, which can result in significant measurementerror. To provide a simple method for selecting the appropriate lengthof the longest line 16, an approximate expression for the line length interms of the maximum permissible linear attenuation A_(max) is:

$\begin{matrix}{_{\max} \approx {- \frac{\ln \left( {{A_{\max}/1} - {\rho }^{2}} \right)}{{Re}\left( {j\; \beta_{0}\sqrt{ɛ_{eff}^{*}}} \right)}}} & (12)\end{matrix}$

where Re(*) denotes the real part of *, and ρ is the reflectioncoefficient due to the transition between the feed line and thesample-covered planar transmission line, which can be approximated as:

$\begin{matrix}{\rho \approx \frac{\sqrt{ɛ_{eff}^{U}} - \sqrt{ɛ_{eff}^{*}}}{\sqrt{ɛ_{eff}^{U}} + \sqrt{ɛ_{eff}^{*}}}} & (13)\end{matrix}$

Where ε_(eff) ^(U) effective permittivity of the feed line, which can beestimated by using a closed-form expression (Gupta et al., MicrostripLines and Slotlines, 1979, Dedham:Artech House). ε_(eff)* can beobtained from (7) by using typical approximate values for d* and c* suchas 0.5 and 2 respectively and the expected range of ε* for the materialto be measured.

An example of how this sensor can be used in conjunction with thecalibration procedure (described in Section 1) is given in Example 1.FIG. 4 shows a photo of the sensor apparatus used in Example 1 anddescribed in this section. FIG. 4 shows hard-gold plated CPW lines 14and 16 that were manufactured on an FR4 laminate substrate 30. The linelength difference, l_(diff), was 10 mm. The CPW lines 14 and 16 wereapproximately 9-mm and 19-mm and were connected to microstrip feed lineson the underside of the board by metal post connections.Microstrip-to-coaxial line transitions 24 were used on each of the feedlines.

For these dimensions, the characteristic impedance of the feed lines isapproximately 50 Ω,

The CPW line is approximately 50Ω when ε′=10. The approximately 19-mmline was chosen by using equation (12), with A_(max)=0.032 (about (30dB)), ε*=53−j27 which is approximately the permittivity of a 25/75%ethanol/water mixture at approximately f=5 GHz.

3. Anisotropy Measurement Technique

A material with a uniaxial permittivity is shown FIG. 3A. The Cartesiancoordinate systems associated with the planar sensor apparatus and thematerial are (x,y,z) and (u,y,w), respectively, where u and w are x andz are rotated by θ radians about the y axis. The relative complexpermittivity tensor of the material, with respect to (x,y,z), is,

$\begin{matrix}{\left\lbrack ɛ^{*} \right\rbrack = {\left\lbrack {ɛ^{\prime} - {j\; ɛ^{''}}} \right\rbrack = \begin{bmatrix}{{ɛ_{\bot}^{*}\cos^{2\;}\theta} + {ɛ_{\parallel}^{*}\sin^{2}\theta}} & 0 & {\left( {ɛ_{\bot}^{*} - ɛ_{\parallel}^{*}} \right)\sin \; \theta \; \cos \; \theta} \\0 & ɛ_{\bot}^{*} & 0 \\{\left( {ɛ_{\bot}^{*} - ɛ_{\parallel}^{*}} \right)\sin \; \theta \; \cos \; \theta} & 0 & {ɛ_{\bot}^{*}\sin^{2}{\theta ɛ}_{\parallel}^{*}\cos^{2}\theta}\end{bmatrix}}} & (14)\end{matrix}$

where ε_(⊥)*=ε_(⊥)′−jε_(⊥)″ and ε_(∥)*=ε_(∥)′−jε_(∥)″ are theperpendicular and parallel components of the permittivity tensor andj=√{square root over (−1)}.

With equation (9) the relative permittivity measured with the CPWconfiguration in FIG. 3B can be expressed as,

$\begin{matrix}{{ɛ_{meas}^{*}(\theta)} = {{{ɛ_{meas}^{\prime}(\theta)} - {j\; {ɛ_{meas}^{''}(\theta)}}} = {- {\frac{1}{d^{*}}\left\lbrack {\left( \frac{\gamma (\theta)}{\beta_{0}} \right)^{2} + c^{*}} \right\rbrack}}}} & (15)\end{matrix}$

where γ(θ) is determined from (2), and d* and c* are determined fromequations (10) and (11) respectively.

For uniaxial materials, referenced to (x,y,z), ε_(meas)*(θ) is afunction of the sample orientation, namely (Torgovnikov, 1993, supra),

ε_(meas)*(θ)=ε_(u)*cos²θ+ε_(w)*sin²θ  (16)

where √{square root over (ε_(u)′)} and √{square root over (ε_(u)″)}, and√{square root over (ε_(w)′)} and √{square root over (ε_(w)′)} representthe measured permittivity with respect to the sample axes. For uniaxialmaterials oriented as in FIG. 3A, ε_(u)*=ε_(⊥)*. The determination ofε_(w)* is less obvious. It was found (Kitazawa and Hayashi, IEEE Trans.Microwave Theory Tech., Volume 29, 1035-1037, 1981; Kobayashi andTerakado, IEEE Trans. Microwave Tech., Volume 27, 769-778, 1979) that,as the conductor thickness, t, of the CPW lines approaches zero,ε_(w)*=√{square root over (ε_(⊥)*ε_(∥)*)}. In practice however, t≠0,which results in a larger proportion of x-directed electric field.ε_(w)* is therefore more influenced by ε_(∥)* than when t=0. The errorin ε_(w)* predicted with the t=0 expression can be large for materialswith considerable anisotropy. To account approximately for the effect oft, we have obtained a simple empirically derived correction to the t=0result, namely,

ε_(w)*=√{square root over (ε_(⊥)*ε_(∥)*)}+(ε_(∥)*−ε_(⊥))(d*d ₀−1)  (17)

where d⁰ is the calibration constant for t=0 and the ratio d*/d⁰directly accounts for the effect of t, in a manner similar to theempirically derived correction presented in (Gupta et al., 1979, supra,p. 278). When ε_(⊥)*=ε_(∥)* or d*=d⁰, ε_(w)* reduces to √{square rootover (ε_(⊥)*ε_(∥)*)}. For CPW, d⁰=0.5 (Gupta, et al., 1979, supra;Roelvink et al, 2013 supra). For conductor-backed CPW (Gupta et al.,1979, supra),

$\begin{matrix}{d^{\; 0} = \left\lbrack {1 + {\frac{K^{\prime}\left( {a/b} \right)}{K\left( {a/b} \right)}\frac{K\left( {{\tanh \left( {\pi \; {a/4}h} \right)}/{\tanh \left( {\pi \; {b/4}h} \right)}} \right)}{K^{\prime}\left( {{\tanh \left( {\pi \; {a/4}h} \right)}/{\tanh \left( {\pi \; {b/4}h} \right)}} \right)}}} \right\rbrack^{- 1}} & (18)\end{matrix}$

where K(*) is the complete elliptic integral and K′(*)=K(√{square rootover (1−(*)²)}). Accurate approximations for K(*)/K′(*) have beenderived (Hillberg, IEEE Trans. Microwave Theory Tech., Volume 17,259-269, 1969). Equation (18) approaches 0.5 as the ratio b/h isdecreased.

From (16), the geometric interpretation of 1/√{square root over(ε_(meas)′(θ))} and 1/√{square root over (ε_(meas)″(θ))} are ellipseswith √{square root over (ε_(u)′)} and √{square root over (ε_(u)″)}, and√{square root over (ε_(w)′)} and √{square root over (ε_(w)′)} as thesemimajor and semiminor axes respectively. This provides a convenientand numerically efficient measurement-based method for determiningε_(⊥)* and ε_(∥)* from ε_(meas)*(θ):1. The permittivity of the samplematerial is measured for a range of known θ . . . 2. The inverse squareroots of ε_(meas)′(θ) and ε_(meas)″(θ) are fitted with ellipses by adirect least squares fitting algorithm (Fizgibbon et al., IEEE Trans.Pattern Analysis and Machine Intelligence, Volume 21, 476-480, 1999)without recourse to iterative numerical fitting procedures. 3. ε_(⊥)*and ε_(∥)* are extracted from the coefficients of the fitted ellipses.This method removes the need to measure carefully prepared and alignedsamples (Akhtar et al., IEEE Trans. Microwave Theory Tech., Volume 54,2011-2022, 2006; Torgovnikov, Dielectric properties of wood andwood-based materials. Wood science, ed. T. E. Timell, 1993,Berlin:Springer-Verlag). Instead, relatively easily prepared andnonaligned samples are measured at a number of known angles, θ.Increasing the number of measured angles increases the accuracy of theinferred ε_(⊥)* and ε_(∥)*. Examples of how this technique can beapplied are given in Example 2.

In addition to the practical applications of the present inventiondescribed above, a further application is in the construction of modelsfor the dielectric heating of materials such as in industrial microwaveor radio frequency heating equipment. Such arrangements can be modeledby using analytical field theory (Rizzi, Mcirowave engineering: Passivecircuits; 1988; New Jersey, USA; Prentice Hall) or with numericaltechniques (COMSOL Multiphysics www.comsol.com), and require theaccurate knowledge of the permittivity of the material to be heated. Thepresent invention discloses an accurate and efficient technique andapparatus for measuring the permittivity of many such materials.

The following examples are presented to illustrate the use of thepresent invention for measuring the permittivity of a material sample.Cyclohexane, ethanol, and various aqueous solutions of ethanol, chickenand beef, and gelatin and sawdust are used as test models in the presentinvention. The examples are intended to illustrate the invention and arenot intended to limit the scope of the defined claims.

Example 1: Permittivity Measurements on Liquids

This example demonstrates how to measure the permittivity of liquidswith the present invention. The scattering parameters were obtained forthree aqueous solutions of ethanol and three reference liquids placed onthe CPW lines over the frequency range 0.5-5 GHz with an Agilent E5071CENA series network analyzer connected to each of the coaxial connectorsas shown in FIG. 5. The scattering parameters without any samplepresent, ε*=1, were also measured. The aqueous solutions of ethanol(purity 99.5%) were mixed by mass with distilled water. Permittivityresults were then calculated by using the technique described inSection 1. The permittivity results were compared to measurementsobtained with an Agilent 85070B coaxial-line probe and reference datafor each liquid (Kaatze, 2007, supra; Green, Measurements of thedielectric relaxation spectra of nine liquids and binary mixtures at 20°C. and microwave frequencies, in Proceedings of the Conference onPrecision Electromagnetic Measurements, 212-213, 1996). All measurementswere made at 20 degrees C.

FIG. 4 shows a photo of hard-gold plated CPW lines 14 and 16 that weremanufactured on an FR4 laminate substrate 30. The line lengthdifference, l_(diff), was approximately 10 mm. The CPW lines 14 and 16were connected to microstrip feed lines 20 on the underside of the boardby metal post 24 connections. The microstrip-to-coaxial line transitions32 were used on each of the feed lines. This forms the sensor apparatusas described in section 2.

Results are presented in FIG. 6 for the calibration constants d* and c*calculated from γ measurements with air, ε₁*=1, and distilled water forε₂* (Kaatze, 2007, supra). The real part of d* is close to 0.5, asexpected for CPW, and essentially constant with frequency, indicatingthat dispersion effects of the lines over this frequency range aresmall.

FIG. 7 shows results for ε* for cyclohexane, a low-permittivityreference liquid that is nondispersive and lossless (Kaatze, 2007,supra). The agreement between the CPW sensor and the reference data isvery good with a maximum relative difference of 1%, while thecoaxial-line probe measurement has a larger error (maximum relativeerror of 5%). FIGS. 8 and 9 show results for ε* for pure ethanol andthree aqueous solutions of ethanol. All results have been fitted withappropriate Debye models (Green, 1996, supra; Gregory and Clarke, NPLReport, MAT 23, National Physical Laboratory, 2009). The CPW results arein excellent agreement with the reference data, with maximum relativeerrors of 5%, 1%, 1% and 3%; for ethanol, 75/25%, 50/50% and 25/75%ethanol/water mixtures, respectively. The maximum relative errors of thecoaxial-line probe measurements were larger in all cases; 13%, 4%, 5%and 4%, respectively. The larger error in the measurements made with thecommercial coaxial-line probe can be explained by the probe-aperturemodel, which contains terms that are measured once by the manufacturerfor a given probe, and are not corrected during subsequent calibrations(Blackham and Pollard, IEEE Trans. Instr. Meas., Volume 46, 1093-1099,1997). Therefore, the calibration procedure for the commercialcoaxial-line probe does not fully account for changes in theprobe-aperture dimensions over time, which can be due to mechanical andthermal stresses. The method of calibration disclosed here does notsuffer from this limitation.

This example demonstrates that very accurate measurements of thepermittivity of materials can be made by using both the calibrationtechnique and the planar transmission-line sensor apparatus describedherein.

Example 2: Anisotropy Measurements on Biological Materials

Because of the difficulty in producing samples with known anisotropicdielectric properties, the anisotropy measurement technique (Section 3)is first demonstrated by using numerical simulation software (COMSOLMultiphysics www.comsol.com). The two-port scattering parameters of twolengths, 20- and 30-mm, of material-loaded conductor-backed CPWtransmission line 14 and 16 at 2 GHz were obtained from simulations. Thepropagation constant, γ(θ), was obtained from the simulated scatteringparameters by using the multiline technique.

The calibration constants in (15) were first obtained from simulationsof two materials with known homogeneous ε* (Roelvink et al, 2013,supra). Several combinations of ε_(⊥)* and ε_(∥)* were considered andfor each combination θ was varied from zero to π/2 in π/24 steps (onequadrant was sufficient due to symmetry). The samples were orientated asshown in FIG. 3. Note, however, that the technique described in Section3 can be used with materials that have different, and unknown, startingangles. The CPW parameters in FIG. 1 were; a=0.4 mm, b=0.8 mm, h=1.6 mm,t=35 μm, and ε_(s)=4. From the calibration procedure (Roelvink et al,2013, supra) d*=0.546 and c*=1.81. (d* and c* are real since thesimulated radiation and conductor losses were negligible Roelvink et al,2013, supra). From (18), d⁰=0.495.

TABLE I COMPARISON OF THE MODELLED AND EXTRACTED PERMITTIVITY AT 2 GHzModelled Extracted Error (%) ∈*_(⊥) ∈*_(∥) ∈*_(⊥) ∈*_(∥) |∈*_(⊥)||∈*_(∥)|  9 − j1.9  27 − j6.8  9.1 − j1.92 27.8 − j7.07 1.61 3.00 30 −j8  35 − j10 29.9 − j8.0  35.9 − j10.0 0.24 0.40 35 − j10 45 − j15 34.9− j10.0 44.7 − j15.0 0.41 0.60 57 − j14 60 − j15 56.8 − j14.1 59.7 −j15.0 0.39 0.45

TABLE II MEASURED PERMITTIVITY TENSOR FOR SEVERAL MEAT SAMPLES AT 2.45GHz (r² VALUES ARE FOR THE FITTED ELLIPSES) r² (1/ r² (1/ Sample ∈*_(⊥)∈*_(∥) √{square root over (∈′)}) √{square root over (∈″)}) Chicken 155.9 − j19.4 58.5 − j20.6 0.97 0.97 Chicken 2 53.4 − j18.5 62.0 − j20.50.89 0.93 Chicken 3 57.5 − j19.4 61.4 − j21.0 0.99 0.99 Chicken 4 50.0 −j16.6 61.9 − j20.3 0.94 0.95 Beef 1 49.0 − j15.2 59.2 − j18.8 0.88 0.89

FIG. 10 compares results for ε_(meas)′(θ), obtained from the simulatedscattering parameters and (15), to results calculated with (16), forseveral different materials. (Note ε_(meas)″(θ) is not shown forbrevity.) Clearly, (16) accurately represents the form of ε_(meas)*(θ).Also included in this figure is the t=0 theoretical result for thelowest three permittivity samples. The appreciable difference betweenthe results demonstrates the need to correct for the conductorthickness. Table I compares permittivity tensor results extracted fromthe fitted elliptical coefficients of 1/√{square root over(ε_(meas)′(θ))} and 1/√{square root over (ε_(meas)″(θ))} (obtained withthe direct least squares fitting algorithm (Fizgibbon et al., IEEETrans. Pattern Analysis and Machine Intelligence, Volume 21, 476-480,1999)) to the modeled ε_(⊥)* and ε_(∥)*. The agreement between modeledand extracted results is clearly very good.

Four chicken breast samples and one beef sirloin tip sample were cut andplaced within a 40×40 mm square sample holder. The sample was thenplaced on a CPW sensor configuration with the same line dimensionsdescribed above, formed on an FR4 laminate substrate. A 56.6-mm diametercircle was inscribed around the sensor. Eighteen radial marks were madeon this circle at π/9 radian (20°) intervals. The corners of the sampleholder were aligned with these marks and the two-port scatteringparameters were measured at each position over the frequency range 0.5-5GHz. The CPW sensor was first calibrated with air (ε′=1) and distilledwater at 25° C. All measurements were made at room temperature, 23° C.

Table II gives the measured uniaxial permittivity tensor for the fivesamples at 2.45 GHz. Also included in the table are the r² values forthe elliptical fits to the measured data. The measured samples exhibitappreciable anisotropy, with |ε_(⊥)/ε_(∥)*| values ranging from 0.81 to0.95. The high r² values show that 1/√{square root over (ε_(meas)′(θ))}and 1/√{square root over (ε_(meas)″(θ))} are accurately modeled byellipses, which supports the assumption that the permittivity tensor forthese materials are uniaxial.

This example demonstrates that accurate and relatively simplemeasurements of the uniaxial permittivity tensor of materials can bemade with the technique disclosed herein. Furthermore, the suitabilityof this technique for measuring the anisotropic dielectric properties ofsemisolid materials is demonstrated. The anisotropic dielectricproperties of materials measured in this way can be used to infer thedifference between fresh and frozen meats, the age of meat, andproperties of wood and wood products.

Example 3: Permittivity Measurement of Biological Materials of DifferentMoisture Contents

Measurements using the CPW were performed on samples of sawdust andgelatin of different moisture content at 25° C. The CPW was connected toan E5071C ENA Network Analyzer and a TRL calibration and two standards(air and distilled water at 25° C.) were used to calibrate the system.Results of the measurements at different frequencies are tabulated belowfor each material and each moisture content:

TABLE 1 Dielectric properties of sawdust at 5.7% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 1.33 1.30 1.31 1.29 1.29 1.28 ∈″ 0.0370.044 0.028 0.036 0.016 0.028

TABLE 2 Dielectric properties of sawdust at 13.1% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 1.68 1.59 1.58 1.56 1.53 1.50 ∈″ 0.160.15 0.14 0.15 0.12 0.12

TABLE 3 Dielectric properties of sawdust at 21.4% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 2.38 2.27 2.22 2.18 2.13 2.03 ∈″ 0.230.29 0.31 0.32 0.31 0.31

TABLE 4 Dielectric properties of sawdust at 32.0% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 4.09 3.84 3.73 3.61 3.47 3.27 ∈″ 0.580.72 0.75 0.81 0.80 0.80

TABLE 5 Dielectric properties of sawdust at 37.6% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 4.99 4.67 4.57 4.41 4.24 4.01 ∈″ 0.690.86 0.90 0.98 0.97 0.98

TABLE 6 Dielectric properties of gelatin slab at 78.3% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 53.9 51.9 51.1 49.9 47.8 45.6 ∈″ 10.110.6 11.3 12.4 13.8 15.1

TABLE 7 Dielectric properties of gelatin slab at 84.5% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 60.1 58.3 57.5 56.1 54.2 51.7 ∈″ 9.410.7 11.6 12.8 14.6 16.5

TABLE 8 Dielectric properties of gelatin slab at 93.3% moisture contentFrequency, GHz 1 2 2.45 3 4 5 ∈′ 67.8 66.9 66.0 64.7 63.2 60.8 ∈″ 7.39.5 10.7 12.3 14.9 17.5

The foregoing detailed examples are for the purpose of illustration.Such detail is solely for that purpose and those skilled in the art canmake variations therein without departing from the spirit and scope ofthe invention.

INDEX OF THE ELEMENTS

-   10. Sensor Apparatus-   14. Short Planar Transmission Line-   16. Long Planar Transmission Line-   18. Board Top Side-   19. Board Bottom Side-   20. Feed Lines-   22. Plated through-hole Vias-   24. Microstrip-to-Coaxial line transitions-   26. Sample Holder-   28. Liquid Sample-   30. Substrate

1. (canceled)
 2. A calibration method for determining complex relativepermittivity ε* of liquids, powders, and semisolid materials frommicrowave scattering parameter measurements with planar transmissionlines comprising: (a) obtaining any liquid, powder, or semisolidmaterial of different geometry, dimensions, and compositions, whereinsaid materials have known or unknown complex relative permittivities;(b) obtaining calibration constants by measuring the propagationconstant γ, of material-loaded planar transmission lines for at leastone radio-frequency and for at least two materials with knownpermittivities by using the expressions$d^{*} = \frac{\gamma_{1}^{2} - \gamma_{2}^{2}}{\beta_{0}^{2}\left( {ɛ_{1}^{*} - ɛ_{2}^{*}} \right)}$${c^{*} = {\left( \frac{\gamma_{1}}{\beta_{0}} \right)^{2} - {d^{*}ɛ_{1}^{*}}}};$(c) determining the relative complex permittivity for each said materialby using the expression$ɛ^{*} = {- {\frac{1}{d^{*}}\left\lbrack {\left( \frac{\gamma}{\beta_{0}} \right)^{2} + c^{*}} \right\rbrack}}$using the calibration constants, d* and c* and the propagation constantγ measured by any technique for determining the propagation constant γfor at least one radio-frequency.
 3. A method for measuring theanisotropic dielectric properties of materials with planar transmissionlines comprising: (a) obtaining any liquid, powder, or semisolidmaterial of different geometry, dimensions, and compositions, whereinsaid materials have known or unknown complex relative permittivitiesthat can be represented by a uniaxial permittivity tensor with theexpression$\left\lbrack ɛ^{*} \right\rbrack = {\left\lbrack {ɛ^{\prime} - {j\; ɛ^{''}}} \right\rbrack = \begin{bmatrix}{{ɛ_{\bot}^{*}\cos^{2\;}\theta} + {ɛ_{\parallel}^{*}\sin^{2}\theta}} & 0 & {\left( {ɛ_{\bot}^{*} - ɛ_{\parallel}^{*}} \right)\sin \; \theta \; \cos \; \theta} \\0 & ɛ_{\bot}^{*} & 0 \\{\left( {ɛ_{\bot}^{*} - ɛ_{\parallel}^{*}} \right)\sin \; \theta \; \cos \; \theta} & 0 & {ɛ_{\bot}^{*}\sin^{2}{\theta ɛ}_{\parallel}^{*}\cos^{2}\theta}\end{bmatrix}}$ where ε_(⊥)*=ε_(⊥)′−jε_(⊥)″ and ε_(∥)*=ε_(∥)′−jε_(∥)″are the perpendicular and parallel components of the permittivitytensor; (b) obtaining calibration constants by measuring the propagationconstant γ, via any technique, of material-loaded planar transmissionlines for at least one radio-frequency and for at least two materialswith known permittivities by using the expressions$d^{*} = \frac{\gamma_{1}^{2} - \gamma_{2}^{2}}{\beta_{0}^{2}\left( {ɛ_{1}^{*} - ɛ_{2}^{*}} \right)}$${c^{*} = {\left( \frac{\gamma_{1}}{\beta_{0}} \right)^{2} - {d^{*}ɛ_{1}^{*}}}};$(c) determining the relative complex permittivity for each said materialby using the expression${ɛ_{meas}^{*}(\theta)} = {{{ɛ_{meas}^{\prime}(\theta)} - {j\; {ɛ_{meas}^{''}(\theta)}}} = {- {\frac{1}{d^{*}}\left\lbrack {\left( \frac{\gamma (\theta)}{\beta_{0}} \right)^{2} + c^{*}} \right\rbrack}}}$by using the calibration constants, d* and c*, and the propagationconstant γ measured via any technique for at least one radio-frequency;(d) determining the permittivity of the sample material for a range ofknown θ with the expression in 1(c) above; (e) fitting the inversesquare roots of ε_(meas)′(θ) and ε_(meas)″(θ) with ellipses by a directleast squares fitting algorithm or other numerical technique; (f)determining √{square root over (ε_(u)′)} and √{square root over(ε_(u)″)}, and √{square root over (ε_(w)′)} and √{square root over(ε_(w)′)} as the semimajor and semiminor axes respectively as thecoefficients of the fitted ellipse; (g) obtaining the perpendicular andparallel components of the permittivity tensor ε_(⊥)* and ε_(∥)* from√{square root over (ε_(u)′)} and √{square root over (ε_(u)″)}, and√{square root over (ε_(w)′)} and √{square root over (ε_(u)″)} with theexpressionε_(w)*=√{square root over (ε_(⊥)*ε_(∥)*)}+(ε_(∥)*−ε_(⊥))(d*d ₀−1) whered⁰ is the calibration constant for t=0 (h) using the perpendicular andparallel components to determine a physical property of an anisotropicmaterial.